The invention lies in the electronics field. More specifically, the invention pertains to a method of suppressing signal noise.
In many cases, undesirable noise is superimposed on a signal, either during the recording (acquisition) of the signal or in the course of transmission. The signals may be one-dimensional, for example voice signals; or two-dimensional, for example stationary images; or three-dimensional, for example picture sequences. In general, the problem of noise suppression may be described as follows:
A noise signal is additively superimposed on a useful signal (i.e., the wanted signal) S0(x,y,t):
S(x,y,t)=S0(x,y,t)+R(x,y,t)
The question is: how to obtain a good estimate for S0(x,y,t) when S(x,y,t) is measured (that is known) and, possibly, when the statistical characteristics of R(x,y,t) are known.
Many noise suppression algorithms presuppose a constant signal and, as a rule, simply average the observed signal. In that case, it is generally assumed that the useful signal has a narrower bandwidth than the noise. The signal-to-noise ratio can be improved by a low-pass filter, such as an averaging filter. However, the assumption of a narrower bandwidth actually results in a problem with such a procedure since the details in a picture or the high frequencies in music are likewise located in the high frequency area. As a rule, they suffer from simple averaging. The requirement is thus for filters with the characteristic of retaining detail.
The most common methods in the prior art are so-called signal-adaptive methods. There, the aim is to detect the signal dynamics in the observed signal in order to average more strongly when major signal changes are present than for minor changes. As a rule, the weightings are in this case applied directly to the measured signal. For example, the normal practice in image processing is to look for specific values which have little signal dynamics. An averaging filter is then applied to these signal dynamics.
By way of example: Averaging of three pixels, which may be described as a homogeneous field.
The disadvantage in that case is that the other points are ignored, even though they likewise contain more or less information which could contribute to improving the estimated values.
It is accordingly an object of the invention to provide a method of suppressing signal noise, which overcomes the above-mentioned disadvantages of the heretofore-known methods of this general type and which suppressing noise in one-dimensional or multidimensional signals, in which the high frequency areas are not so heavily attenuated, so that corresponding details are retained.
With the foregoing and other objects in view there is provided, in accordance with the invention, a method of suppressing noise in a signal, which comprises: measuring a noisy signal S(x,y,t) and carrying out a plurality of estimates for a corresponding noise-free useful signal S0(x,y,t) on a basis of the measurement of the noisy signal S(x,y,t);
individually assigning each estimated value S0(1), S0(1), S0(2), . . . , S0(k) obtained for each point (x,y,t) in carrying out the plurality of estimates a preference xcex1j(x,y,t), where j=1,2, . . . , k; and k is an integer; and forming a new estimated value {overscore (S)}0(x,y,t) for the useful signal from the estimated values S0(1), S0(2), . . . , S0(k) by arithmetic averaging weighted by the preference xcex1j(x,y,t).
In other words, the object of the invention is satisfied in that a plurality of estimates for the noise-free useful signal are carried out on the basis of a measurement of the noisy signal, and each of the estimated values obtained for each point is individually assigned a preference, and a new estimated value for the useful signal is then formed from the estimated values by arithmetic averaging weighted by the preference.
In accordance with an added feature of the invention, the estimated value {overscore (S)}0(x,y,t) is calculated with the following formula:                                           S            o                    _                ⁡                  (                      x            ,            y            ,            t                    )                    =                        ∑                      j            =            1                    k                ⁢                                                            α                j                            ⁡                              (                                  x                  ,                  y                  ,                  t                                )                                      A                    ⁢                                    S              o                              (                j                )                                      ⁡                          (                              x                ,                y                ,                t                            )                                            ,    where        A    =                  ∑                  j          =          1                k            ⁢                                    α            j                    ⁡                      (                          x              ,              y              ,              t                        )                          .            
In accordance with an additional feature of the invention, the preference xcex1j(x,y,t) is determined by considering statistical characteristics of the noise.
In accordance with a further feature of the invention, the signal is a one-dimensional signal S(t) and the method comprises determining one of the estimated values with an earlier-measured value, determining a further estimated value with a later-measured value, and determining the weighting factors or preference values xcex1j associated with the estimated values as a function of the signal.
In accordance with a preferred embodiment, the following estimated values and preferences are defined for the one-dimension signal:                                                         S                              (                1                )                                      ⁡                          (                              t                0                            )                                =                      xe2x80x83                    ⁢                                    1              2                        ⁡                          [                                                S                  ⁡                                      (                                          t                      0                                        )                                                  +                                  S                  ⁡                                      (                                                                  t                        0                                            +                      1                                        )                                                              ]                                      ,                                                                    α              1                        ⁡                          (                              t                0                            )                                =                      xe2x80x83                    ⁢                      1                                          [                                                      S                    ⁡                                          (                                              t                        0                                            )                                                        -                                                            S                                              (                        1                        )                                                              ⁡                                          (                                              t                        0                                            )                                                                      ]                            2                                      ;                                                                    S                              (                2                )                                      ⁢                          t              0                                =                      xe2x80x83                    ⁢                                    1              2                        ⁡                          [                                                S                  ⁡                                      (                                          t                      0                                        )                                                  +                                  S                  ⁡                                      (                                                                  t                        0                                            -                      1                                        )                                                              ]                                      ;                                                                    α              2                        ⁡                          (                              t                0                            )                                =                      xe2x80x83                    ⁢                      1                                          [                                                      S                    ⁡                                          (                                              t                        0                                            )                                                        -                                                            S                                              (                        2                        )                                                              ⁡                                          (                                              t                        0                                            )                                                                      ]                            2                                      ;                                                                    S                              (                3                )                                      ⁢                          t              0                                =                      xe2x80x83                    ⁢                      S            ⁡                          (                              t                0                            )                                      ;                                                      α            3                    ⁡                      (                          t              0                        )                          =                  xe2x80x83                ⁢                              1                          σ              n              2                                ⁢                      xe2x80x83                    ⁢          and                                                              S            _                    ⁡                      (                          t              0                        )                          =                  xe2x80x83                ⁢                                            ∑                              i                =                1                            3                        ⁢                          xe2x80x83                        ⁢                                          α                i                            ·                                                S                                      (                    i                    )                                                  ⁡                                  (                                      t                    0                                    )                                                                                        ∑                              i                =                1                            3                        ⁢                          xe2x80x83                        ⁢                          α              j                                          
where "sgr"n2 is selected from the group of consisting of a statistical variance of the noise and a value to be set by the user.
In accordance with another feature of the invention, the signal is a two-dimensional signal S(x,y) and the method comprises determining further estimated values using adjacent measured signal values and are weighted by signal-dependent weighting factors or preference values xcex1j.
In accordance with a preferred embodiment of the invention, mean values S(1)(x0,y0); . . . ; S(8)(x0,y0) are formed from the measured signal value S(x0,y0) of the two-dimensional signal, and respective adjacent measured signal values S(x0xe2x88x921,y0); S(x0+1,y0); S(x0xe2x88x921,y0+1); S(x0+1,y0+1); S(x0+1,y0xe2x88x921); S(x0+1,y0xe2x88x921); S(x0,y0+1); S(x0,y0xe2x88x921) are weighted by a factor xcex1j, where             α      j        =          1                        [                                    S              ⁢                              xe2x80x83                            ⁢                              (                                                      x                    0                                    ,                                      y                    0                                                  )                                      -                                          S                                  (                  j                  )                                            ⁢                              xe2x80x83                            ⁢                              (                                                      x                    0                                    ,                                      y                    0                                                  )                                              ]                2              ;
and the estimated value is determined from the mean value of the estimated values S(1)(x0,y0); . . . ; S(8)(x0,y0) weighted in such a way and the measured value S(x0,y0) weighted by a factor xcex19 which is predetermined by the user or is calculated using the formula             α      9        =          1              σ        n        2              ,
where "sgr"n2 represents a statistical variance of the noise.
In other words, for two-dimensional signals it is particularly preferable for the mean values to be formed from the measured signal value and the eight respective adjacent measured signal values, and to be weighted in each case by a factor which is defined as the reciprocal of the square of the difference between the measured signal value and the respective mean value and for the new estimated value for the noise-free signal then to be determined from the mean value of the estimated values weighted by this factor and the measured value weighted by a factor which is predetermined by the user or is calculated using the statistical variance of the noise.
In accordance with again an added feature of the invention, the signal is a three-dimensional signal S(x0,y0,t0), such as a television picture signal, and the method comprises using an estimated result of a previous sampling time {overscore (S)}(x0,y0,t0xe2x88x921) as the first estimated value S(1)(x0,y0,t0), using the mean value of a present pixel and of the points located in front of and behind the present pixel on the same line (median) {S(x0xe2x88x921,y0,t0), S(x0,y0,t0), S(x0+1,y0,t0) as the second estimated value S(2)(x0,y0,t0), and using the value of the current pixel S(x0,y0,t0) as the third estimated value S(3)(x0,y0,t0), and determining the final estimated value by averaging the first, second and third estimated values {overscore (S)}(x0,y0,t0), weighted by one of signal-dependent weighting factors and preference values xcex1j.
In accordance with again a preferred embodiment of the invention, the estimated values are weighted as follows:                               S                      (            1            )                          ⁡                  (                                    x              0                        ,                          y              0                        ,                          t              0                                )                    ⁢              xe2x80x83            ⁢      with      ⁢              xe2x80x83            ⁢              1                              [                                                            S                                      (                    1                    )                                                  ⁡                                  (                                                            x                      0                                        ,                                          y                      0                                        ,                                          t                      0                                                        )                                            -                              S                ⁢                                  xe2x80x83                                ⁢                                  (                                                            x                      0                                        ,                                          y                      0                                        ,                                          t                      0                                                        )                                                      ]                    2                      ;                                S                      (            2            )                          ⁡                  (                                    x              0                        ,                          y              0                        ,                          t              0                                )                    ⁢              xe2x80x83            ⁢      with      ⁢              xe2x80x83            ⁢              1                              [                                                            S                                      (                    2                    )                                                  ⁡                                  (                                                            x                      0                                        ,                                          y                      0                                        ,                                          t                      0                                                        )                                            -                              S                ⁢                                  xe2x80x83                                ⁢                                  (                                                            x                      0                                        ,                                          y                      0                                        ,                                          t                      0                                                        )                                                      ]                    2                      ;                                S                      (            3            )                          ⁡                  (                                    x              0                        ,                          y              0                        ,                          t              0                                )                    ⁢              xe2x80x83            ⁢      with      ⁢              xe2x80x83            ⁢              1                  σ          n          2                      ⁢          xe2x80x83      
where "sgr"n2 represents a statistical variance of the noise or a value to be set by a user.
In other words, for three-dimensional signals, for example television pictures, it is particularly preferable for the estimated result of the previous sampling time to be used as the first estimated value, for the mean value of the current pixel and of those points which are located in front of and behind it on the same line to be used as the second estimated value, and for the value of the current pixel to be used as the third estimated value, while the three estimated values are weighted for the determination of the final estimated value of the noise-free signal by averaging from the three estimated values with the given factors:
The estimated result of the previous sampling time with the reciprocal of the square of the difference of the previous estimated value and of the current measured value, the mean value of the current pixel and of those points which are located in front of and behind it on the same line with the reciprocal of the square of the difference of this mean value and of the current measured value, and the actual measured value with the reciprocal of the statistical variance of the noise or a value which can be set by the user.
In accordance with a concomitant feature of the invention, an upper and a lower limit are defined for the preference values xcex1j and weighting factors.       1          σ      n      2        .
Other features which are considered as characteristic for the invention are set forth in the appended claims.
Although the invention is illustrated and described herein as embodied in a method for suppressing noise in signals, it is nevertheless not intended to be limited to the details shown, since various modifications and structural changes may be made therein without departing from the spirit of the invention and within the scope and range of equivalents of the claims.
The construction and method of operation of the invention, however, together with additional objects and advantages thereof will be best understood from the following description of specific embodiments when read in connection with the accompanying drawings.